Answer: \( \frac{6(3b + 2)}{(3b+2)(3b-2)} \).
Here's Why...
To solve the expression \( \frac{9ab(6b+4)}{108ab^3 - 48ab} \), we can follow these steps:
1. Factor out common terms in the numerator:
\( 9ab(6b + 4) = 54ab^2 + 36ab \)
2. Factor out common terms in the denominator:
\( 108ab^3 - 48ab = 12ab(9b^2 - 4) = 12ab(3b+2)(3b-2) \)
3. Simplify the expression:
\( \frac{54ab^2 + 36ab}{12ab(3b+2)(3b-2)} \)
4. Cancel out common factors where possible:
\( \frac{18b + 12}{3(3b+2)(3b-2)} \)
5. Final simplified expression:
\( \frac{6(3b + 2)}{(3b+2)(3b-2)} \)
By simplifying the expression step by step and canceling out common factors, we arrive at the final simplified expression \( \frac{6(3b + 2)}{(3b+2)(3b-2)} \).
